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a). Find stationary point: Stationary point is the point at which the gradient equals zero. So first we must find the gradient and the set it to zero and solve: dy/dx= 2x-54x^(-1/2); now we set this to ze...

Using integration by parts split it into v'=(1/x^3) and u=ln(x). v=-1/2x^2 and u'=1/x. Integral ln(x)/(x^3) = u*v - Integral u'*v = -ln(x)*1/2x^2 - 1/4x^2 + c

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expressio...

Due to notation difficulties, S = integral sign. This is a straightforward integration question, firstly we expand the brackets:

f'(x)=3x^2 - 3x f(x)=S(3x^2 - 3x)dx f(x)=3/3x^3 - 3/2x^2 + C f(x)=x^...

y-(any value of the function)=0.5(x-(any value in the domain))

e.g. Point with point A being (1,14) The answer would be y-14=0.5(x-1)